On the Use of Quality Diversity Algorithms for The Traveling Thief Problem
This work addresses a complex real-world optimization problem for researchers and practitioners in combinatorial optimization, but it is incremental as it applies an existing QD method to a known integrated problem.
The paper tackles the Traveling Thief Problem (TTP), an integrated optimization problem combining the Traveling Salesperson Problem (TSP) and Knapsack Problem (KP), by applying Quality Diversity (QD) algorithms to investigate their inter-dependency and generate high-quality solutions. It shows that this QD approach provides insights into solution distributions and improves best-known solutions for several benchmark TTP instances.
In real-world optimisation, it is common to face several sub-problems interacting and forming the main problem. There is an inter-dependency between the sub-problems, making it impossible to solve such a problem by focusing on only one component. The traveling thief problem~(TTP) belongs to this category and is formed by the integration of the traveling salesperson problem~(TSP) and the knapsack problem~(KP). In this paper, we investigate the inter-dependency of the TSP and the KP by means of quality diversity~(QD) approaches. QD algorithms provide a powerful tool not only to obtain high-quality solutions but also to illustrate the distribution of high-performing solutions in the behavioural space. We introduce a MAP-Elite based evolutionary algorithm using well-known TSP and KP search operators, taking the TSP and KP score as the behavioural descriptor. Afterwards, we conduct comprehensive experimental studies that show the usefulness of using the QD approach applied to the TTP. First, we provide insights regarding high-quality TTP solutions in the TSP/KP behavioural space. Afterwards, we show that better solutions for the TTP can be obtained by using our QD approach and it can improve the best-known solution for a number of TTP instances used for benchmarking in the literature.